Design of optimal nonlinear PI compensators

In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by (linear) proportional and integral (PI) compensators are considered. For such systems five and six-parameter nonlinear compensators are proposed. The parameters of the proposed compensators are tuned by solving an optimization problem. To ensure the stability of the closed-loop system, a term is added to the cost function of the optimization problem; the added term is a measure of the stability of the linearized closed-loop system in a neighborhood of the system equilibrium point. The superiority of the proposed nonlinear PI compensators over linear PI compensators is demonstrated in an example